Is There a Procedure to Reduce the Size of my Eyes?

There is no non surgical way to do this, but I would check with your doctor to find out if your thyroid function is normal.

I assume that is you on the left and the actress on the right. You say you do not have thyroid problems but do not say if you have had the blood tests for it. You need to have the T4 and T3 levels checked and compared to the TSH level to know for sure. If the blood tests are normal you may be a candidate for a lateral canthopexy. Normally the outer corners of the eyes lie 2mm above the level of the inner corners of the eyes. I cannot tell from the angle of the right photo if that is the case with you. If it is not the canthopexy or canthoplasty can raise it and make the eyelid opening outline more almond shaped and less round.

Both pictures show very attractive eyes. You are right that an orbital decompression is too extreme. It is not a cosmetic operation. There is the possibility of using injectable fillers that could make the eye look deeper set. Also, cosmetics can do be used  to change the appearance of the eyes.